Metrology method and apparatus, computer program and lithographic system

ABSTRACT

Disclosed are a method, computer program and associated apparatuses for metrology. The method includes acquiring inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by inspection of a corresponding target structure formed using a lithographic process; and performing an unsupervised cluster analysis on said inspection data, thereby partitioning said inspection data into a plurality of clusters in accordance with a metric. In an embodiment, a cluster representative can be identified for each cluster. The cluster representative may be reconstructed and the reconstruction used to approximate the other members of the cluster.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit to EP Application EP15166833.2 which isincorporated by reference herein in its entirety.

BACKGROUND Field of the Invention

The present invention relates to methods and apparatuses for metrologyusable, for example, in the manufacture of devices by lithographictechniques.

Background Art

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,including part of, one, or several dies) on a substrate (e.g., a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. In lithographic processes, itis desirable frequently to make measurements of the structures created,e.g., for process control and verification. Various tools for makingsuch measurements are known, including scanning electron microscopes,which are often used to measure critical dimension (CD), and specializedtools to measure overlay, a measure of the accuracy of alignment of twolayers in a device. Overlay may be described in terms of the degree ofmisalignment between the two layers, for example reference to a measuredoverlay of 1 nm may describe a situation where two layers are misalignedby 1 nm.

Recently, various forms of scatterometers have been developed for use inthe lithographic field. These devices direct a beam of radiation onto atarget and measure one or more properties of the scatteredradiation—e.g., intensity at a single angle of reflection as a functionof wavelength; intensity at one or more wavelengths as a function ofreflected angle; or polarization as a function of reflected angle—toobtain a diffraction image or pattern from which a property of interestof the target can be determined.

In order that the radiation that impinges on to the substrate isdiffracted, an object with a specific shape is printed on to thesubstrate and is often known as a scatterometry target or simply target.As mentioned above, it is possible to determine the actual shape of ascatterometry object using a cross-section scanning electron microscopeand the like. However, this involves a large amount of time, effort andspecialized apparatus and is less suited for measurements in aproduction environment because a separate specialized apparatus isrequired in line with normal apparatus in, for example, a lithographiccell.

Determination of the property of interest may be performed by varioustechniques: e.g., reconstruction of the target by iterative approachessuch as rigorous coupled wave analysis or finite element methods;library searches; and principal component analysis.

To perform such reconstructions, a profile may be used. To make theprofile more robust, good nominal values for parameters (representativeof the data as a whole) should be chosen.

It is desirable to provide a method which can help with choosing suchnominal values.

SUMMARY OF THE INVENTION

The invention in a first aspect provides a method of metrologycomprising: acquiring inspection data, said inspection data comprising aplurality of inspection data elements, each inspection data elementhaving been obtained by inspection of a corresponding target structureformed using a lithographic process; and performing an unsupervisedcluster analysis on said inspection data, thereby partitioning saidinspection data into a plurality of clusters in accordance with ametric.

The invention in a second aspect provides a metrology apparatus operableto perform the method of the first aspect. The invention in a thirdaspect provides a lithographic system comprising a metrology apparatusof the second aspect.

The invention further provides a computer program comprising processorreadable instructions which, when run on suitable processor controlledapparatus, cause the processor controlled apparatus to perform themethod of the first aspect, and a computer program carrier comprisingsuch a computer program. The processor controlled apparatus may comprisethe metrology apparatus of the second aspect or the lithographic systemof the third aspect.

Further features and advantages of the invention, as well as thestructure and operation of various embodiments of the invention, aredescribed in detail below with reference to the accompanying drawings.It is noted that the invention is not limited to the specificembodiments described herein. Such embodiments are presented herein forillustrative purposes only. Additional embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying drawings in which:

FIG. 1 depicts a lithographic apparatus;

FIG. 2 depicts a lithographic cell;

FIG. 3 depicts a first scatterometer;

FIG. 4 depicts a second scatterometer;

FIG. 5 is a flowchart depicting a first example process forreconstruction of a structure from scatterometer measurements;

FIG. 6 is a flowchart depicting a second example process forreconstruction of a structure from scatterometer measurements;

FIG. 7 depicts a cluster representation map, showing the partitioning oftargets into clusters using a method according to an embodiment of theinvention; and

FIG. 8 is a flowchart depicting a method of metrology according to anembodiment of the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Before describing embodiments of the invention in detail, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatusincludes an illumination optical system (illuminator) IL configured tocondition a radiation beam B (e.g., ultraviolet (UV) radiation or deepultraviolet (DUV) radiation), a patterning device support or supportstructure (e.g., a mask table) MT constructed to support a patterningdevice (e.g., a mask) MA and connected to a first positioner PMconfigured to accurately position the patterning device in accordancewith certain parameters; a substrate table (e.g., a wafer table) WTconstructed to hold a substrate (e.g., a resist coated wafer) W andconnected to a second positioner PW configured to accurately positionthe substrate in accordance with certain parameters; and a projectionoptical system (e.g., a refractive projection lens system) PS configuredto project a pattern imparted to the radiation beam B by patterningdevice MA onto a target portion C (e.g., including one or more dies) ofthe substrate W.

The illumination optical system may include various types of opticalcomponents, such as refractive, reflective, magnetic, electromagnetic,electrostatic or other types of optical components, or any combinationthereof, for directing, shaping, or controlling radiation.

The patterning device support holds the patterning device in a mannerthat depends on the orientation of the patterning device, the design ofthe lithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The patterning device support can use mechanical, vacuum, electrostaticor other clamping techniques to hold the patterning device. Thepatterning device support may be a frame or a table, for example, whichmay be fixed or movable as required. The patterning device support mayensure that the patterning device is at a desired position, for examplewith respect to the projection system. Any use of the terms “reticle” or“mask” herein may be considered synonymous with the more general term“patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

As here depicted, the apparatus is of a transmissive type (e.g.,employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g., employing a programmable mirror array of a typeas referred to above, or employing a reflective mask).

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDincluding, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may include an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL mayinclude various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the patterning device support (e.g., mask tableMT), and is patterned by the patterning device. Having traversed thepatterning device (e.g., mask) MA, the radiation beam B passes throughthe projection optical system PS, which focuses the beam onto a targetportion C of the substrate W, thereby projecting an image of the patternon the target portion C. With the aid of the second positioner PW andposition sensor IF (e.g., an interferometric device, linear encoder, 2-Dencoder or capacitive sensor), the substrate table WT can be movedaccurately, e.g., so as to position different target portions C in thepath of the radiation beam B. Similarly, the first positioner PM andanother position sensor (which is not explicitly depicted in FIG. 1) canbe used to accurately position the patterning device (e.g., mask) MAwith respect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan.

Patterning device (e.g., mask) MA and substrate W may be aligned usingmask alignment marks M1, M2 and substrate alignment marks P1, P2.Although the substrate alignment marks as illustrated occupy dedicatedtarget portions, they may be located in spaces between target portions(these are known as scribe-lane alignment marks). Similarly, insituations in which more than one die is provided on the patterningdevice (e.g., mask) MA, the mask alignment marks may be located betweenthe dies. Small alignment markers may also be included within dies, inamongst the device features, in which case it is desirable that themarkers be as small as possible and not require any different imaging orprocess conditions than adjacent features. The alignment system, whichdetects the alignment markers is described further below.

Lithographic apparatus LA in this example is of a so-called dual stagetype which has two substrate tables WTa, WTb and two stations—anexposure station and a measurement station—between which the substratetables can be exchanged. While one substrate on one substrate table isbeing exposed at the exposure station, another substrate can be loadedonto the other substrate table at the measurement station and variouspreparatory steps carried out. The preparatory steps may include mappingthe surface control of the substrate using a level sensor LS andmeasuring the position of alignment markers on the substrate using analignment sensor AS. This enables a substantial increase in thethroughput of the apparatus.

The depicted apparatus can be used in a variety of modes, including forexample a step mode or a scan mode. The construction and operation oflithographic apparatus is well known to those skilled in the art andneed not be described further for an understanding of the presentinvention.

As shown in FIG. 2, the lithographic apparatus LA forms part of alithographic system, referred to as a lithographic cell LC or alithocell. The lithographic cell LC may also include apparatus toperform pre- and post-exposure processes on a substrate. Conventionallythese include spin coaters SC to deposit resist layers, developers DE todevelop exposed resist, chill plates CH and bake plates BK. A substratehandler, or robot, RO picks up substrates from input/output ports I/O1,I/O2, moves them between the different process apparatus and deliversthen to the loading bay LB of the lithographic apparatus. These devices,which are often collectively referred to as the track, are under thecontrol of a track control unit TCU which is itself controlled by thesupervisory control system SCS, which also controls the lithographicapparatus via lithography control unit LACU. Thus, the differentapparatus can be operated to maximize throughput and processingefficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. If errors are detected, adjustments may be made to exposures ofsubsequent substrates, especially if the inspection can be done soon andfast enough that other substrates of the same batch are still to beexposed. Also, already exposed substrates may be stripped andreworked—to improve yield—or discarded, thereby avoiding performingexposures on substrates that are known to be faulty. In a case whereonly some target portions of a substrate are faulty, further exposurescan be performed only on those target portions which are good.

An inspection apparatus is used to determine the properties of thesubstrates, and in particular, how the properties of differentsubstrates or different layers of the same substrate vary from layer tolayer. The inspection apparatus may be integrated into the lithographicapparatus LA or the lithocell LC or may be a stand-alone device. Toenable most rapid measurements, it is desirable that the inspectionapparatus measure properties in the exposed resist layer immediatelyafter the exposure. However, the latent image in the resist has a verylow contrast—there is only a very small difference in refractive indexbetween the parts of the resist which have been exposed to radiation andthose which have not—and not all inspection apparatus have sufficientsensitivity to make useful measurements of the latent image. Thereforemeasurements may be taken after the post-exposure bake step (PEB) whichis customarily the first step carried out on exposed substrates andincreases the contrast between exposed and unexposed parts of theresist. At this stage, the image in the resist may be referred to assemi-latent. It is also possible to make measurements of the developedresist image—at which point either the exposed or unexposed parts of theresist have been removed—or after a pattern transfer step such asetching. The latter possibility limits the possibilities for rework offaulty substrates but may still provide useful information.

FIG. 3 depicts a scatterometer which may be used in the presentinvention. It comprises a broadband (white light) radiation projector 2which projects radiation onto a substrate W. The reflected radiation ispassed to a spectrometer detector 4, which measures a spectrum 10(intensity as a function of wavelength) of the specular reflectedradiation. From this data, the structure or profile giving rise to thedetected spectrum may be reconstructed by processing unit PU, e.g. byRigorous Coupled Wave Analysis and non-linear regression or bycomparison with a library of simulated spectra as shown at the bottom ofFIG. 3. In general, for the reconstruction the general form of thestructure is known and some parameters are assumed from knowledge of theprocess by which the structure was made, leaving only a few parametersof the structure to be determined from the scatterometry data. Such ascatterometer may be configured as a normal-incidence scatterometer oran oblique-incidence scatterometer.

Another scatterometer that may be used with the present invention isshown in FIG. 4. In this device, the radiation emitted by radiationsource 2 is collimated using lens system 12 and transmitted throughinterference filter 13 and polarizer 17, reflected by partiallyreflected surface 16 and is focused onto substrate W via a microscopeobjective lens 15, which has a high numerical aperture (NA), preferablyat least 0.9 and more preferably at least 0.95. Immersion scatterometersmay even have lenses with numerical apertures over 1. The reflectedradiation then transmits through partially reflecting surface 16 into adetector 18 in order to have the scatter spectrum detected. The detectormay be located in the back-projected pupil plane 11, which is at thefocal length of the lens system 15, however the pupil plane may insteadbe re-imaged with auxiliary optics (not shown) onto the detector. Thepupil plane is the plane in which the radial position of radiationdefines the angle of incidence and the angular position defines azimuthangle of the radiation. The detector is preferably a two-dimensionaldetector so that a two-dimensional angular scatter spectrum of asubstrate target 30 can be measured. The detector 18 may be, forexample, an array of charge-coupled device (CCD) or complementarymetal-oxide semiconductor (CMOS) sensors, and may use an integrationtime of, for example, 40 milliseconds per frame.

A reference beam is often used for example to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the beam splitter 16 part of it is transmitted through the beamsplitter as a reference beam towards a reference mirror 14. Thereference beam is then projected onto a different part of the samedetector 18 or alternatively on to a different detector (not shown).

A set of interference filters 13 is available to select a wavelength ofinterest in the range of, say, 405-790 nm or even lower, such as 200-300nm. The interference filter may be tunable rather than comprising a setof different filters. A grating could be used instead of interferencefilters.

The detector 18 may measure the intensity of scattered light at a singlewavelength (or narrow wavelength range), the intensity separately atmultiple wavelengths or integrated over a wavelength range. Furthermore,the detector may separately measure the intensity of transversemagnetic- and transverse electric-polarized light and/or the phasedifference between the transverse magnetic- and transverseelectric-polarized light.

Using a broadband light source (i.e. one with a wide range of lightfrequencies or wavelengths—and therefore of colors) is possible, whichgives a large etendue, allowing the mixing of multiple wavelengths. Theplurality of wavelengths in the broadband preferably each has abandwidth of Δλ, and a spacing of at least 2 Δλ, (i.e. twice thebandwidth). Several “sources” of radiation can be different portions ofan extended radiation source which have been split using fiber bundles.In this way, angle resolved scatter spectra can be measured at multiplewavelengths in parallel. A 3-D spectrum (wavelength and two differentangles) can be measured, which contains more information than a 2-Dspectrum. This allows more information to be measured which increasesmetrology process robustness.

The target 30 on substrate W may be a 1-D grating, which is printed suchthat after development, the bars are formed of solid resist lines. Thetarget 30 may be a 2-D grating, which is printed such that afterdevelopment, the grating is formed of solid resist pillars or vias inthe resist. The bars, pillars or vias may alternatively be etched intothe substrate. This pattern is sensitive to chromatic aberrations in thelithographic projection apparatus, particularly the projection systemPL, and illumination symmetry and the presence of such aberrations willmanifest themselves in a variation in the printed grating. Accordingly,the scatterometry data of the printed gratings is used to reconstructthe gratings. The parameters of the 1-D grating, such as line widths andshapes, or parameters of the 2-D grating, such as pillar or via widthsor lengths or shapes, may be input to the reconstruction process,performed by processing unit PU, from knowledge of the printing stepand/or other scatterometry processes.

As described above, the target is on the surface of the substrate. Thistarget will often take the shape of a series of lines in a grating orsubstantially rectangular structures in a 2-D array. The purpose ofrigorous optical diffraction theories in metrology is effectively thecalculation of a diffraction spectrum that is reflected from the target.In other words, target shape information is obtained for CD (criticaldimension) uniformity and overlay or focus metrology. Overlay metrologyis a measuring system in which the overlay of two targets is measured inorder to determine whether two layers on a substrate are aligned or not.Focus metrology determines the focus (and/or dose) setting used whenforming the target. CD uniformity is simply a measurement of theuniformity of the grating on the spectrum to determine how the exposuresystem of the lithographic apparatus is functioning. Specifically, CD,or critical dimension, is the width of the object that is “written” onthe substrate and is the limit at which a lithographic apparatus isphysically able to write on a substrate.

Using a scatterometer, such as that described above in combination withmodeling of a target structure such as the target 30 and its diffractionproperties, measurement of the shape and other parameters of thestructure can be performed in a number of ways. In a first type ofprocess, represented by FIG. 5, a diffraction pattern based on a firstestimate of the target shape (a first candidate structure) is calculatedand compared with the observed diffraction pattern. Parameters of themodel are then varied systematically and the diffraction re-calculatedin a series of iterations, to generate new candidate structures and soarrive at a best fit. In a second type of process, represented by FIG.6, diffraction spectra for many different candidate structures arecalculated in advance to create a ‘library’ of diffraction spectra. Thenthe diffraction pattern observed from the measurement target is comparedwith the library of calculated spectra to find a best fit. Both methodscan be used together: a coarse fit can be obtained from a library,followed by an iterative process to find a best fit.

Throughout the description of FIG. 5 and FIG. 6, the term ‘diffractionimage’ will be used, on the assumption that the scatterometer of FIG. 3or 4 is used. Diffraction image is an example of an inspection dataelement within the context of this disclosure. The skilled person canreadily adapt the teaching to different types of scatterometer, or evenother types of measurement instrument.

FIG. 5 is a flowchart of the steps of a method of measurement of thetarget shape and/or material properties, described in summary. The stepsare as follows, and are then described in greater detail thereafter:

-   -   402—Measure Diffraction Image;    -   403—Define Model Recipe;    -   404—Estimate Shape Parameters p₁ ⁽⁰⁾, p₂ ⁽⁰⁾, p₃ ⁽⁰⁾, . . . ;    -   406—Calculate Model Diffraction Image;    -   408—Compare Measured v Calculated Image;    -   410—Calculate Merit Function;    -   412—Generate Revised Shape Parameters p₁ ⁽¹⁾, p₂ ⁽¹⁾, p₃ ⁽¹⁾, .        . . ;    -   414—Report Final Shape Parameters        The target will be assumed for this description to be periodic        in only 1 direction (1-D structure). In practice it may be        periodic in 2 directions (2-dimensional structure), and the        processing will be adapted accordingly.

402: The diffraction image of the actual target on the substrate ismeasured using a scatterometer such as those described above. Thismeasured diffraction image is forwarded to a calculation system such asa computer. The calculation system may be the processing unit PUreferred to above, or it may be a separate apparatus.

403: A profile is established which defines a parameterized model of thetarget structure in terms of a number of parameters pi (p1, p2, p3 andso on). These parameters may represent for example, in a 1D periodicstructure, the angle of a side wall, the height or depth of a feature,the width of the feature. Properties of the target material andunderlying layers are also represented by parameters such as refractiveindex (at a particular wavelength present in the scatterometry radiationbeam). Specific examples will be given below. Importantly, while atarget structure may be defined by dozens of parameters describing itsshape and material properties, the profile will define many of these tohave fixed values, while others are to be variable or ‘floating’parameters for the purpose of the following process steps. Moreover,ways will be introduced in which parameters can be permitted to varywithout being fully independent floating parameters. For the purposes ofdescribing FIG. 5, only the variable parameters are considered asparameters pi. The profile also defines the settings of the measurementradiation for a given target structure and how to estimate the parametervalues by fitting the inspection data to the model.

404: A model target shape is estimated by setting initial values pi(0)for the floating parameters (i.e. p1(0), p2(0), p3(0 and so on). Eachfloating parameter will be generated within certain predeterminedranges, as defined in the recipe.

406: The parameters representing the estimated shape, together with theoptical properties of the different elements of the model, are used tocalculate the scattering properties, for example using a rigorousoptical diffraction method such as RCWA or any other solver of Maxwellequations. This gives an estimated or model diffraction image of theestimated target shape.

408, 410: The measured diffraction image and the model diffraction imageare then compared and their similarities and differences are used tocalculate a “merit function” for the model target shape.

412: Assuming that the merit function indicates that the model needs tobe improved before it represents accurately the actual target shape, newparameters p1(1), p2(1), p3(1), etc. are estimated and fed backiteratively into step 406. Steps 406-412 are repeated.

In order to assist the search, the calculations in step 406 may furthergenerate partial derivatives of the merit function, indicating thesensitivity with which increasing or decreasing a parameter willincrease or decrease the merit function, in this particular region inthe parameter space. The calculation of merit functions and the use ofderivatives is generally known in the art, and will not be describedhere in detail.

414: When the merit function indicates that this iterative process hasconverged on a solution with a desired accuracy, the currently estimatedparameters are reported as the measurement of the actual targetstructure.

The computation time of this iterative process is largely determined bythe forward diffraction model used, i.e. the calculation of theestimated model diffraction image using a rigorous optical diffractiontheory from the estimated target structure. If more parameters arerequired, then there are more degrees of freedom. The calculation timeincreases in principle with the power of the number of degrees offreedom, although this can be alleviated if finite differences are usedto approximate the Jacobian. The estimated or model diffraction imagecalculated at 406 can be expressed in various forms. Comparisons aresimplified if the calculated image is expressed in the same form (e.g.,spectrum, pupil image) as the measured image generated in step 402.

FIG. 6 is a flowchart of the steps of an alternative method ofmeasurement of the target shape and/or material properties, described insummary. In this method, a plurality of model diffraction images fordifferent estimated target shapes (candidate structures) are calculatedin advance and stored in a library for comparison with a realmeasurement. The underlying principles and terminology are the same asfor the process of FIG. 5. The steps are as follows, and are thendescribed in greater detail thereafter:

-   -   502—Generate Library;    -   503—Define Model Recipe;    -   504—Sample Shape Parameters p₁ ⁽⁰⁾, p₂ ⁽⁰⁾, p₃ ⁽⁰⁾, . . . ;    -   506—Calculate and Store Model Diffraction Image;    -   508—New Sample Shape Parameters p₁ ⁽¹⁾, p₂ ⁽¹⁾, p₃ ⁽¹⁾, . . . ;    -   510—Measure Diffraction Image;    -   512—Compare Measured Image v Library Images;    -   514—Report Final Shape Parameters;    -   516—Refine Shape Parameters.

502: The process of generating the library begins. A separate librarymay be generated for each type of target structure. The library may begenerated by a user of the measurement apparatus according to need, ormay be pre-generated by a supplier of the apparatus.

503: A profile is established which defines a parameterized model of thetarget structure in terms of a number of parameters pi (p1, p2, p3 andso on). Considerations are similar to those in step 503 of the iterativeprocess.

504: A first set of parameters p1(0), p2(0), p3(0), etc. is generated,for example by generating random values of all the parameters, eachwithin its expected range of values.

506: A model diffraction image is calculated and stored in a library,representing the diffraction image expected from a target shaperepresented by the parameters.

508: A new set of shape parameters p1(1), p2(1), p3(1), etc. isgenerated. Steps 506-508 are repeated tens, hundreds or even thousandsof times, until the library which comprises all the stored modeleddiffraction images is judged sufficiently complete. Each stored imagerepresents a sample point in the multi-dimensional parameter space. Thesamples in the library should populate the sample space with asufficient density that any real diffraction image will be sufficientlyclosely represented.

510: After the library is generated (though it could be before), thereal target 30 is placed in the scatterometer and its diffraction imageis measured.

512: The measured image is compared with the modeled images stored inthe library to find the best matching image. The comparison may be madewith every sample in the library, or a more systematic searchingstrategy may be employed, to reduce computational burden.

514: If a match is found then the estimated target shape used togenerate the matching library image can be determined to be theapproximate object structure. The shape parameters corresponding to thematching sample are output as the measured shape parameters. Thematching process may be performed directly on the model diffractionsignals, or it may be performed on substitute models which are optimizedfor fast evaluation.

516: Optionally, the nearest matching sample is used as a startingpoint, and a refinement process is used to obtain the final parametersfor reporting. This refinement process may comprise an iterative processvery similar to that shown in FIG. 5, for example.

Whether refining step 516 is needed or not is a matter of choice for theimplementer. If the library is very densely sampled, then iterativerefinement may not be needed because a good match will always be found.On the other hand, such a library might be too large for practical use.A practical solution is thus to use a library search for a coarse set ofparameters, followed by one or more iterations using the merit functionto determine a more accurate set of parameters to report the parametersof the target substrate with a desired accuracy. Where additionaliterations are performed, it would be an option to add the calculateddiffraction images and associated refined parameter sets as new entriesin the library. In this way, a library can be used initially which isbased on a relatively small amount of computational effort, but whichbuilds into a larger library using the computational effort of therefining step 516. Whichever scheme is used, a further refinement of thevalue of one or more of the reported variable parameters can also beobtained based upon the goodness of the matches of multiple candidatestructures. For example, the parameter values finally reported may beproduced by interpolating between parameter values of two or morecandidate structures, assuming both or all of those candidate structureshave a high matching score.

The computation time of this iterative process is largely determined bythe forward diffraction model at steps 406 and 506, i.e. the calculationof the estimated model diffraction image using a rigorous opticaldiffraction theory from the estimated target structure shape.

The creation of a profile involves multiple refinements of the profile,wherein the physical model is gradually adjusted to best represent theinspection data. The inspection data may comprise inspection dataelements. The inspection data elements may be images, diffraction images(if diffraction based scatterometery is being used), spectra or pupilimages; or else may be reconstructed parameter values obtained from suchdiffraction images etc. Each of the inspection data elements may beobtained by inspection of a corresponding target structure, e.g., usinga scatterometer such as those described above. Each of these inspectiondata elements may be described by a plurality of intensity values. Theadjustments are typically based upon the results of reconstructions.Reconstructions, as described, fit the model to the inspection data,thereby transforming the inspection data elements into parameter values.At the beginning of the procedure, reconstructions may fail asuncertainties may be large. It may therefore be more effective toreconstruct only one or a few measurements rather than the complete setof data.

To make a profile more robust, the nominal parameter values for theprofile should be well chosen. Ideally, to properly estimate thesenominal parameter values, many target structures should bereconstructed. However, this may take too much time. Consequently, itmay be the case that only one or a few target structures arereconstructed to provide nominal parameter values. Should the selectedtarget structure(s) not be a good representation of the targetstructures generally, there may be a significant bias to the measuredvalues and the profile will not be optimal.

To obtain nominal parameter values, one or more target structure(s) maybe randomly selected for reconstruction. A typical refinement is to onlychoose target structures which lie within a band between 30 mm and 120mm from the center of a substrate (target structures too close to thecenter or edge are not considered ideal). However, it can bedemonstrated that there may be significant variation in the values forcertain parameters even for target structures which meet this criterion.Using the example of mid-CD (CD as measured at half the height of theobject) as the parameter being considered, it can be shown that targetstructures within the 30 mm-120 mm band may still have a standarddeviation of between 2σ and 2.5σ away from the mean value. Selecting oneof these target structures for reconstruction to find nominal parametervalues would be far from ideal.

It is therefore proposed to perform an unsupervised clustering ormachine learning algorithm to partition the inspection data intoclusters in such a way that inspection data elements within a clusterare more similar than the inspection data elements in other clusters. Inunsupervised clustering, the data being clustered is unlabeled data. Inthis way unsupervised clustering is distinct from supervised learningtechniques such as linear discriminant analysis, in which a linearcombination of features is found which characterizes or separates two ormore known classes of data. Analysis of the clustering enables moreinformed choices of target structures which better represent averagevalues for the parameter(s) being considered.

A particular clustering algorithm needs to be given a criterion tomeasure the similarity of inspection data elements. To do this a metric,or distance function, may be determined. A metric is a function whichdefines a distance between the inspection data elements comprised withinthe inspection data. According to some algorithms, the smaller thisdistance is between two inspection data elements, the more similar thetwo inspection data elements are. Other clustering algorithms useprobability distributions to determine the clusters. Suitable clusteringalgorithms may include a k-means algorithm or a Gaussian-mixture modelbased algorithm (e.g., Expectation-Maximization (EM) clustering), forexample.

In an embodiment, the clustered data may be displayed to a user as awafer map, wherein the target structures on a wafer (or over multiplewafers, e.g., a lot of wafers) are shown clustered according to theclustering of the inspection data elements by the clustering algorithm.This “cluster representation” map may optionally show each clusterrepresentative, which are described below. In this way, the user canidentify groups of target structures which are similar to each other.

FIG. 7 shows an example of such a cluster representation map. It showswafer (or substrate) 600 comprising fields 610. Comprised within thefields 610 are target structures grouped into five clusters 620 a-620 e,as indicated by the shading, such that target structures with likeshading are part of the same cluster. Each cluster also has a clusterrepresentative 630 circled.

As just mentioned, in certain embodiments, cluster representatives maybe identified. A cluster representative is a target structure of acluster which best represents the cluster dataset. The clusterrepresentative will be a target structure within the cluster for whichthe value for the parameter(s) under consideration is closest to average(e.g., closest to the mean value for that parameter).

Many clustering algorithms use cluster centers to model the data, suchthat objects in the dataset are each allocated to a cluster comprisingthe nearest cluster center, in terms of the metric (there may be manyrefinements on this basic concept depending upon the actual clusteringalgorithm used). Where cluster centers are not used, they can be simplycalculated from the clusters. The distribution across clusters may thenbe iteratively refined until the distribution no longer changes. It isproposed that each cluster representative may be chosen to be the targetstructure which corresponds closest to the cluster center for thatcluster.

To use a specific example of a clustering algorithm, the k-meansalgorithm (or a variation thereon) may comprises iterations of:

-   -   assigning each object to a cluster having the nearest cluster        center (cluster centers may be randomly chosen or otherwise for        the first iteration); and    -   calculating the mean of each cluster, to use as an updated        cluster center for the next iteration.

This is repeated until convergence on a solution (a cluster distributionwhich no longer changes each iteration). As such, each cluster centerwill, following convergence, be the mean of the data points of itscorresponding cluster.

Applying such a clustering algorithm to inspection data, comprising aplurality of inspection data elements, will yield clusters of inspectiondata elements (each corresponding to the target structure from which themeasurement was taken). It will also yield, for each cluster, a clustercenter representing the mean of that cluster (specifically, in anembodiment where the inspection data comprises diffraction images, amean of all the intensity values describing each inspection dataelement). The cluster representative, in each case, can then be taken tobe the target structure which best corresponds to the mean valuesdescribed by the cluster center. This may be the target structurecorresponding to the inspection data element which is nearest to thecluster center, according to the metric.

Other clustering algorithms form clusters by representing theprobability density function of observed variables as a mixture ofmultivariate normal densities. Mixture models use an expectationmaximization (EM) algorithm to fit data, which assigns posteriorprobabilities to each component density with respect to eachobservation. Clusters are assigned by selecting the component thatmaximizes the posterior probability. Clustering using Gaussian mixturemodels is sometimes considered a soft clustering method. The posteriorprobabilities for each point indicate that each data point has someprobability of belonging to each cluster. Like k-means clustering,Gaussian mixture modeling uses an iterative algorithm that converges toa local optimum. In k-means clustering, a point either belongs to acluster or not, i.e. it is a binary assignment. It is a hard decision.In mixture model based clustering, a data point only belongs to clusterup to a degree (that degree can vary between 0 and 1); therefore a pointmay belong to multiple clusters, in each case with a different degree.It is a soft decision. Gaussian mixture modeling may be more appropriatethan k-means clustering when clusters have different sizes andcorrelation within them. Like k-means clustering, mixture modellingyields natural cluster centers which can be used to derive clusterrepresentatives.

In an embodiment, the cluster representatives can then be reconstructed.The estimated values for the parameters being considered, resultant fromthe reconstruction, can be used as the nominal values for a profile, asthese will best represent the data for its corresponding cluster.

FIG. 8 is a flowchart of the steps of a method for piecewise approximatereconstruction of a plurality of target structures according to anexemplary embodiment. Conventionally, when measuring the targetstructures on wafer, all target structures are inspected to obtain theinspection data and then each inspection data element (corresponding toa target structure) is reconstructed. Therefore, a reconstruction isperformed for each target structure. The method described by theflowchart greatly reduces the number of reconstructions needed tomeasure a wafer. The steps are as follows, and are then described ingreater detail thereafter:

-   -   700—Start;    -   710—Input data: Inspection data elements, Profile, Number of        Clusters;    -   720—Cluster Inspection Data elements;    -   730—Reconstruct Cluster Representatives;    -   740—Approximate Reconstruction for Remaining Target structures;    -   750—End

Input data 710 comprises the inspection data element set, obtained from,for example, measurements of all target structures on a wafer, a subsetof these target structures or measurements of target structures overmultiple wafers, e.g, a lot. The input data also comprises a profile(e.g., a CD profile) for performing a reconstruction of the targetstructures and (optionally) a value for the number of clusters which theinspection data is to be divided into.

At step 720, the inspection data elements are clustered, and clusterrepresentatives identified, using one of the methods already described.

At step 730, the cluster representatives are reconstructed (using theprofile), for example by using one of the methods of FIG. 5 or FIG. 6.

At step 740, the reconstruction of each of the remaining targetstructures in each cluster is approximated, based upon thereconstruction of the corresponding cluster representative or upon all(or a subset) of the cluster representatives.

In an embodiment, step 740 may comprise a linear reconstruction. Ingeneral, reconstruction of a target structure is a non-linear problem,such that the relationship between the inspection data and the parametervalues being estimated is non-linear. However, the similarity ofinspection data within a single cluster means that, for this dataset,the relationship can be approximated to a linear relationship, greatlysimplifying the reconstruction. The nature of the clustering means thatthis linear approximation will be good for inspection data within acluster. In an embodiment, the linearization may be a Jacobianlinearization with the reconstruction of the cluster representativedefining the equilibrium point.

In an embodiment, a single approximate reconstruction is performed foreach (non-representative) target, based upon the cluster representativeof the cluster of which it is a member (in k-means or other hardclustering) or for which it is most likely a member (in probabilisticclustering). However, in other embodiments separate approximatereconstructions (which are very quick and simple) can be performed foreach single (non-representative) target based on each of the identifiedcluster representatives of the whole dataset. Therefore each target willhave a number of reconstructed values for each parameter attributed toit, each of these values being resultant from a different clusterrepresentative. The final reconstructed value for each parameter canthen be a weighted average of each of these approximate reconstructedvalues. In probabilistic clustering, this weighted average may dependupon the probability distribution, and therefore the likelihood that thetarget is a member of each particular cluster. Values derived fromreconstruction of cluster representatives of clusters for which thetarget has a high likelihood of being a member will have a higherweighting than those derived from reconstruction of clusterrepresentatives of clusters for which the target has a low likelihood ofbeing a member. For k-means type clustering, the weighted average maydepend on the distance (according to the metric) between the target andeach cluster representative.

The method of FIG. 8 requires a value for the number of clusters as aninput (other embodiments may not require the number of clusters to beinput, and instead will determine this automatically). As the methodreconstructs a cluster representative for each cluster, it is apparentthat the number of cluster representatives will impact the time tomeasure a wafer (or any selection of target structures). However, toofew clusters will mean that the approximation at step 740 may becompromised. It can be shown that the number of clusters should bechosen to be between 3 and 8, and more preferably between 4 and 6.Specifically, a good choice for the number of clusters has been shown tobe 5 or 6. This has been demonstrated by performing a fingerprintmatching method, which measures the similarity of parameter valueestimates using scatterometery methods as described herein, whencompared to measurements of the parameter using another measurement tool(e.g., a scanning election microscope). It can be shown that thedifference between the two measurements falls steadily as the number ofclusters increases from 1 to 5, but remains fairly constant thereafter.In other words, there is nothing much to be gained from having more thanfive clusters, the resultant wafer map being stable when performing themethod of FIG. 8 with any number of clusters over 4. Where 5 clustersare chosen, only 5 reconstructions will be necessary to approximate afull wafer map with negligible error. Where a wafer has 176 targetstructures, the reconstruction of the whole wafer can be performed 35(176/5) times faster than in the conventional way.

In an alternative embodiment, the number of clusters is not input at thebeginning of the algorithm, and instead the algorithm learns the numberof clusters. In such an embodiment, the steps of FIG. 8 are performedmultiple times for ascending numbers of clusters, starting at (forexample) 1 or 2 to a chosen maximum value. For example, the method ofFIG. 8 might be performed up to 10 times, for each number of clustersbetween 1 and 10. As the number of clusters increases, the withincluster distance metric will gradually fall. The method is performed forascending numbers of clusters up to a point where the within clusterdistance falls below a defined threshold.

The methods described above have performed the clustering on rawinspection data, which has not been processed (or has undergone minimalprocessing). This means that the clustering has been performed on the(e.g., diffraction) images obtained via inspection. As an alternative tothis, at least one reconstruction can be performed (using a profile);this reconstruction can be used to approximately reconstruct theremaining target structures. The clustering can then be performed basedon the (approximately) reconstructed parameter values. In other words,the clustering can be performed on the inspection images, on the(approximated) reconstructed parameter values from the inspectionimages, or on a combination of these. For the avoidance of doubt, theterms inspection data and inspection data elements in the context ofthis disclosure include the diffraction images, transformed diffractionimages (see below) and/or reconstructed parameter values from thediffraction images.

One disadvantage of clustering based on the inspection images is thatthe clustering will be mainly influenced by the most sensitive featuresin the target structure to which the inspection image corresponds, thatis the features which have the greatest impact on the inspection imageshould they change. It is therefore proposed, in an embodiment should itbe considered necessary, to apply a transformation to the inspectionimages before clustering. For example, a projection on one or moreprincipal components associated to smaller eigenvalues would make itpossible to cluster on weaker target structure features. Differentcluster representation maps, such as that shown on FIG. 7, can beproduced for clusters obtained from the same target structures, bothwithout transformation and with different transformations (projectionson different one or more components). These cluster representation mapscan be compared and analyzed.

The methods described herein result in improved efficiency of themeasurement procedure (flow) in terms of speed, reliability of theresults and quality of the end result including the robustness of thefinal profile.

While the target structures described above are metrology targetstructures specifically designed and formed for the purposes ofmeasurement, in other embodiments, properties may be measured on targetstructures which are functional parts of devices formed on thesubstrate. Many devices have regular, grating-like structures. The terms‘target structure grating’ and ‘target structure’ as used herein do notrequire that the structure has been provided specifically for themeasurement being performed. Further, pitch P of the metrology targetstructures is close to the resolution limit of the optical system of thescatterometer, but may be much larger than the dimension of typicalproduct features made by lithographic process in the target structureportions C. In practice the lines and/or spaces of the gratings withinthe target structures may be made to include smaller structures similarin dimension to the product features.

In association with the physical grating structures of the targetstructures as realized on substrates and patterning devices, anembodiment may include a computer program containing one or moresequences of machine-readable instructions describing methods ofmeasuring target structures on a substrate and/or analyzing measurementsto obtain information about a lithographic process. This computerprogram may be executed for example within unit PU in the apparatus ofFIG. 3 or FIG. 4 and/or the control unit LACU of FIG. 2. There may alsobe provided a data storage medium (e.g., semiconductor memory, magneticor optical disk) having such a computer program stored therein. Where anexisting metrology apparatus, for example of the type shown in FIG. 3 orFIG. 4, is already in production and/or in use, the invention can beimplemented by the provision of updated computer program products forcausing a processor to perform the methods as described above and asclaimed.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.,having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g., having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description by example, and not oflimitation, such that the terminology or phraseology of the presentspecification is to be interpreted by the skilled artisan in light ofthe teachings and guidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

The invention claimed is:
 1. A method of metrology comprising: acquiring inspection data, the inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by inspection of a corresponding target structure formed using a lithographic process in a lithographic system; performing an unsupervised cluster analysis on the inspection data, thereby partitioning the inspection data into a plurality of clusters in accordance with a metric; determining a representative inspection data element for each of the plurality of clusters, each representative inspection data element corresponding to a representative target structure formed using the lithographic process; performing a reconstruction operation to obtain at least one reconstructed parameter value from each representative inspection data element, the at least one reconstructed parameter value comprising a value for at least one parameter of the corresponding representative target structure formed using the lithographic process; and performing a targeted reconstruction operation of each target structure, other than the representative target structures, based upon the at least one reconstructed parameter value of at least one of the representative target structures, wherein the targeted reconstruction operation for each target structure is based upon the at least one reconstructed parameter value for the representative target structure of the cluster of which that target structure is a member.
 2. The method as claimed in claim 1, wherein: the inspection data comprises measured intensities within spectra or images, and the spectra or images comprise diffraction spectra or images obtained by the inspection using a scatterometer.
 3. The method as claimed in claim 1, wherein the inspection data comprises values for at least one parameter of the corresponding target structure as determined by a subsequent reconstruction operation on the inspection data.
 4. The method as claimed in claim 1, wherein the partitioning of the inspection data is performed in accordance with a relative distance, as defined by the metric, between each inspection data element and a cluster center of each cluster.
 5. The method as claimed in claim 1, wherein the partitioning of the inspection data is performed in accordance with one or more statistical distribution models, such that each cluster is defined as comprising the inspection data elements belonging to the same distribution.
 6. The method as claimed in claim 1, wherein each representative inspection data element is a closest to an average inspection data element, in terms of the metric, for its corresponding cluster.
 7. The method as claimed in claim 1, wherein the at least one reconstructed parameter value for each representative target structure is used to derive a nominal value for at least one model parameter in subsequent reconstruction operations.
 8. The method as claimed in claim 1, wherein the targeted reconstruction operation for each target is further based upon a weighted average of reconstructed parameter values for all, or a subset of, the representative target structures.
 9. The method as claimed in claim 1, wherein a number of clusters is automatically learned.
 10. The method as claimed in claim 9, wherein the number of clusters is automatically learned by: performing the clustering analysis multiple times, each time partitioning the inspection data into n clusters, wherein n is chosen to be between 3 and 8 and is increased each time a cluster analysis is performed, determining an average within cluster distance according to the metric for each cluster analysis, and selecting the cluster analysis for which the average within cluster distance meets a threshold criterion.
 11. The method as claimed in claim 1, wherein the acquiring inspection data comprises: inspecting the target structures by illuminating each one of the target structures with measurement radiation and detecting the radiation scattered by each one of the target structures.
 12. A metrology apparatus comprising: a support configured to support a substrate having a plurality of target structures thereon, the plurality of target structures formed using a lithographic process in a lithographic system; an optical system used in inspection of the plurality of target structures; and a processor configured to: acquire inspection data, the inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by the inspection of a corresponding target structure; perform an unsupervised cluster analysis on the inspection data, thereby partitioning the inspection data into a plurality of clusters in accordance with a metric; determine a representative inspection data element for each of the plurality of clusters, each representative inspection data element corresponding to a representative target structure formed using the lithographic process; perform a reconstruction operation to obtain at least one reconstructed parameter value from each representative inspection data element, the at least one reconstructed parameter value comprising a value for at least one parameter of the corresponding representative target structure formed using the lithographic process; and for each of the plurality of clusters, perform a second reconstruction operation of each target structure, other than the corresponding representative target structure, based at least on the at least one reconstructed parameter value of the corresponding representative target structure, wherein the targeted reconstruction operation for each target is based upon a weighted average of reconstructed parameter values for all, or a subset of, the representative target structures.
 13. A lithographic system comprising: a lithographic apparatus comprising: an illumination optical system configured to illuminate a pattern; and a projection optical system configured to project an image of the pattern onto a substrate; and a metrology apparatus configured to: acquire inspection data, the inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by inspection of a corresponding target structure formed using the lithographic apparatus; perform an unsupervised cluster analysis on the inspection data, thereby partitioning the inspection data into a plurality of clusters in accordance with a metric; determine a representative inspection data element for each of the plurality of clusters, each representative inspection data element corresponding to a representative target structure formed using the lithographic apparatus; perform a reconstruction operation to obtain at least one reconstructed parameter value from each representative inspection data element, the at least one reconstructed parameter value comprising a value for at least one parameter of the corresponding representative target structure formed using the lithographic apparatus; and perform a targeted reconstruction operation of each target structure, other than the representative target structures, based upon the at least one reconstructed parameter value of at least one of the representative target structures, wherein the targeted reconstruction operation for each target structure is based upon the at least one reconstructed parameter value for the representative target structure of the cluster of which that target structure is a member.
 14. A computer program comprising processor readable instructions which, when run on a suitable processor controlled apparatus, cause the processor controlled apparatus to perform a method comprising: acquiring inspection data, the inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by inspection of a corresponding target structure formed using a lithographic process in a lithographic system; performing an unsupervised cluster analysis on the inspection data, thereby partitioning the inspection data into a plurality of clusters in accordance with a metric; determining a representative inspection data element for each of the plurality of clusters, each representative inspection data element corresponding to a representative target structure formed using the lithographic process; performing a reconstruction operation to obtain at least one reconstructed parameter value from each representative inspection data element, the at least one reconstructed parameter value comprising a value for at least one parameter of the corresponding representative target structure formed using the lithographic process; and performing a targeted reconstruction operation of each target structure, other than the representative target structures, based upon the at least one reconstructed parameter value of at least one of the representative target structures, wherein the targeted reconstruction operation for each target structure is based upon the at least one reconstructed parameter value for the representative target structure of the cluster of which that target structure is a member.
 15. A computer program carrier comprising a computer program comprising processor readable instructions which, when run on a suitable processor controlled apparatus, cause the processor controlled apparatus to perform a method comprising: acquiring inspection data, the inspection data comprising a plurality of inspection data elements, each inspection data element having been obtained by inspection of a corresponding target structure formed using a lithographic process in a lithographic system; performing an unsupervised cluster analysis on the inspection data, thereby partitioning the inspection data into a plurality of clusters in accordance with a metric; determining a representative inspection data element for each of the plurality of clusters, each representative inspection data element corresponding to a representative target structure formed using the lithographic process; performing a reconstruction operation to obtain at least one reconstructed parameter value from each representative inspection data element, the at least one reconstructed parameter value comprising a value for at least one parameter of the corresponding representative target structure formed using the lithographic process; and performing a targeted reconstruction operation of each target structure, other than the representative target structures, based upon the at least one reconstructed parameter value of at least one of the representative target structures, wherein the targeted reconstruction operation for each target is based upon a weighted average of reconstructed parameter values for all, or a subset of, the representative target structures. 